Being an aggressive mob, it's going to be hard to kill it as it is about the same speed as you and it can destroy buildings.
Its fur is used for crafting a Fur Hat, the most powerful chapka in the game.
The Mammoth can kill you in three hits if you lack any means of protection or regeneration.
When farming for fur, make sure that you have atleast 2 empty inventory slots or one of your slots have raw meat or one of them already have mammoth fur. Otherwise, the fur will disappear as the raw meat is prioritized over the fur.
You can kill a mammoth the same way you would kill an arctic fox, though keep in mind that it can destroy fires. An easier way is to lead the mammoth to the forest (you are faster, and the mammoth cannoth destroy buildings) then kill it the same way you would kill a wolf. Alternatively, you can use a sled to kill a mammoth. You can't stay between the border of the forest and winter because the mammoth will follow you into the forest biome.
Another way is to lead the mammoth to the same spot where you would kill a dragon (the row of 3 diamonds in the cave). You could use a wall, but the mammoth has twice as much health as a dragon, and a higher building damage (150 instead of 90). If you choose use a wall, use a reidite wall, or use an amethyst wall and a wrench.